SOLUTION: Use quadratic formula to solve word problem f(x)=-0.5x^2+4x+19 models the number of people in the United States, f(x), in millions, receiving food stamps x years after 1990.In

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Question 666699: Use quadratic formula to solve word problem
f(x)=-0.5x^2+4x+19
models the number of people in the United States, f(x), in millions, receiving food stamps x years after 1990.In which year(s)were 20 million people receiving food stamps? Round to the nearest year(s).
I did this
20= -0.5x^2+4x+19
-20 -20
=-0.5x^2+4x-1
I then used quadratic formula
x= -4+/-sqrt 4^2-4(-0.5)(-1)
-2(-0.5)
which gave me -4+/-sqrt14
-1
I don't know if I'm doing it right or how to get the year(s) for that either.
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Use quadratic formula to solve word problem
f(x)=-0.5x^2+4x+19 models the number of people in the United States, f(x), in millions, receiving food stamps x years after 1990. In which year(s)were 20 million people receiving food stamps? Round to the nearest year(s).
I did this
20= -0.5x^2+4x+19
-20 -20
=-0.5x^2+4x-1 ***** = 0 (don't just have the equal sign)
------------------
I then used quadratic formula
x= -4+/-sqrt(4^2-4(-0.5)(-1))
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -0.5x%5E2%2B4x%2B-1+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%284%29%5E2-4%2A-0.5%2A-1=14.

Discriminant d=14 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-4%2B-sqrt%28+14+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%284%29%2Bsqrt%28+14+%29%29%2F2%5C-0.5+=+0.258342613226059
x%5B2%5D+=+%28-%284%29-sqrt%28+14+%29%29%2F2%5C-0.5+=+7.74165738677394

Quadratic expression -0.5x%5E2%2B4x%2B-1 can be factored:
-0.5x%5E2%2B4x%2B-1+=+%28x-0.258342613226059%29%2A%28x-7.74165738677394%29
Again, the answer is: 0.258342613226059, 7.74165738677394. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-0.5%2Ax%5E2%2B4%2Ax%2B-1+%29


--------------
x1 rounds to 0 years.
Add to 1990 --> 1990
=====================
x2 rounds to 8 years
--> 1998
==========
==========
-2(-0.5)
which gave me -4+/-sqrt14
-1